ITA - Prova de Seleção 1S2021 - Ex16 Matemática

@import url(https://fonts.googleapis.com/css?family=Source+Sans+Pro:300,400,600,700); Instituto Tecnológico de Aeronáutica

Programa de Programação em Engenharia de Infraestrutura Aeronáutica / Programa de Programação em Engenharia Aeronáutica e Mecânica

Prova de Seleção \u2013 1° semestre de 2021\u2013 Questões de Matemática

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16 - Which of the following numbers is prime? (Qual dos números a seguir é primo)

(a) 51

(b) 91

(c) 181

(d) 289

(e) 1001

Resolução:

"Para descobrirmos se um \ufeff n u \u02ca m e r o número n u \u02ca m e r o \ufeff é primo devemos verificar quais os divisores de \ufeff n u \u02ca m e r o número n u \u02ca m e r o \ufeff . Podemos fazer isso utilizando os critérios de divisibilidade, ou seja, dividindo \ufeff n u \u02ca m e r o número n u \u02ca m e r o \ufeff pelos números \ufeff p r i m o s : 2 , 3 , 5 primos: 2, 3, 5 p r i m o s : 2 , 3 , 5 \ufeff . Iremos parar de dividir \ufeff n u \u02ca m e r o número n u \u02ca m e r o \ufeff por \ufeff p r i m o s primos p r i m o s \ufeff quando o valor do quociente for menor que o do divisor . Caso nenhum resto das divisões seja igual a zero , o número será considerado primo. [1]"

Iniciaremos pelo número \ufeff 1001 1001 1 0 0 1 \ufeff - nota-se que não é possível dividir por 2, pois o dividendo é impar. Então tentamos dividir \ufeff 1001 / 3 1001 / 3 1 0 0 1 / 3 \ufeff -> também não é possível, pois se somarmos seus algoritmos \ufeff 1 + 0 + 0 + 1 = 2 1 + 0 + 0 + 1 = 2 1 + 0 + 0 + 1 = 2 \ufeff (então 2 não é divisível por 3). O número \ufeff 1001 1001 1 0 0 1 \ufeff não é divisível por 5 pois o seu último algoritmo também deveria ser 5. Tentamos dividir então \ufeff 1001 / 7 1001 / 7 1 0 0 1 / 7 \ufeff : <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHIAAAEQCAYAAABsliCYAAALLElEQVR4nO2dO3Kj3BpFt27doUgOXBrBYQR2J46c3gxCKemsQ2dOUGiG0JGThhGIEagcCOZyboDQg4cNkhCwtVeVqv5fIDdoCTgcvsfEWmshRs9/+t4AcR0kkgSJJEEiSZBIEiSSBIkkQSIBAClWzgQTZ4W07005k+uITFfwnAkmEw9R/UqIPAfOZILJ7uU4HqLKb67Num22oWt2P4jJdy8Hqw5+Lf+99A+kKwezZfzTWlg5MyxjAMbAnc+BzQZBHOB5toGfrLGYnrNum224DQ+vLtx59bJNECDGHA/T6uUXYc8msb6BBWCNH+7+27Vh1Zq+sQAs3NOlSeiW3m+zbpttaLQvxrdJ6882pHL7r8f5IhPfGhjrJ9YevtCqLzFflq9btSz/XJt122zDjzvTucjQrduv63D+NXK6wNqWT3NlEnzFAMwrfpXWneJhDgAbbNO267bZhp5JV3gLULNf16H7UWu6xQYA5g+o2ofZowEQ4ytpue6IiN6XiAG4fxaV+3UNdPvRORE+AwBw8fLU3b8ikR2Trt4QADD+b3ToUSK7JcL7Mgbg4k/HF/LuRU4fkI1RtpWzJkk2usHjrOW6YyD6RHZWfen0aARuckTOkI1RvlAeo+TXj/wmuc26QyfFKhuqwv/dtcabiJzi16sBEOCtMDeVXz8Ov9g26w6c6H03O9XdLccJ59+CJjZ0XevuXgbZDa/J3/PDo5vr0LrIZmBgdst3MzLlG/g267bZhu/35doTAtkEAGxHEzklLhB59IVXvgpfehJa3zVHy401bs0X13jdlttQy5VFJn72o+pyyq/AxFqFQ+4n6uEjWXd3094luv0gQSJJkMhvieB9+5D4+NXmgfb1/66ukSToiCRBIkmQSBIkkgSJJEEiSZBIEiSShB5E9hdWf1XapihE3j4FwqnYuTSN4DnOyXfgraLGuSgXpwycQ29h9VeifYpCFi1Q+4nIw+w5iyYwros5NgiCGMHyGcFXCPvR4FH6jR6XNaPjsPrLOS9FIUuDMNb33d1nk9JyU3wInj/TbPhMdVAiuw6rv5izUhR2D7/dcP9DLYqs+ce+SZ8oM5zBzg3C6i/mjBSFyHtGABdhk9PjBQxG5C3C6m/O7sd5VnByHrzl/mn0w+llsFPmNmH1tyXF6n9LxMZH0sREGiFKAGCL7edfLIMYMM2P5EGIvFVY/U3ZHVFu2OwMk/57w3NhJGzmj0AKNPoDTa7x3ZJHwp2T19gn3w12jgY4J283HewkNgkP4Z1NBjv9H5E3DKu/FfszzOYTnvd5WLDZAADiv+/wvoDHlw8sKnd6iunTB9YhMHkOsHyPsPjpFNv8F9gF7YbYw6L+iNynz//w+vHIzO+rG8TH9jtqvXVY/Y2YLtaw2T366St0AQDGT2CtxXoxRTZl6WBVKlmSIspGgLWJv8f0emrNN3Q8txwpIu8d+clyEwPABm+el733+ILfi6cz9iXG8nmGJQzc3dxlNlUJoOk96HmnlSvQQ1j95VyYolA72Els6LvWmKO/ZUyL3BWlDNAwmJkdcRkSSYJEkiCRJEgkCRJJgkSSIJEkSCQJEkmCRJIgkSRIJAkSSYJEkiCRJEgkCRJJgkSScGYUXYooKharnuHpadrDMgHgzCi6PHC2KoLs1suEtVZRdDToGkmCRJIgkSRIJAkSSYJEkiCRJEgkCRJJgkSSIJEkSCQJEkmCRJIgkSRIJAkSSUJvIttV1U8Rec6+Sv9kMoHjeChV/Tr5SMsuAGOnlwCTfQxO3qH8qAhfqTD9oSA8jNl1QTf7z1fV5Tst6ncfsT29iGxTVX8vpSA4qexIcF4XAAYGUHg3p6rk53dlQCvKbJ7VBYCDgQ92EnzVlgGd4mEOABts82vlGV0AWBiOyKqq+ukWG6C2Xuns0QCI8VWMXb5D+qvXemFVfXFKbyIvrqovTujt1HpaLjpBErpAsMTzbASd6gbIQK6ReVV9F0CM5fvuFn76gGw8s62cKEiykRAeZzfb0MEyEJEF9uJmyMYzXyiPZ/LuPcNuUXgremoE2rSq/hS/Xg2AAG+F823eW4OpX8gl9JCNlWLlzLJbjbqq+vbjSE4Eb/KcSTO7BqKbAEFctW6hC0AQIIaBcefZKfrsLgAjoJ95iJZV9ZPQ+sfzsTDWuFXdCS7sAjBilB9JwjAHO6I1EkmCRJIgkSRIJAkSSYJEkiCRJEgkCRJJgkSSIJEkDEpkqzSCNMKqIo2g/JzzTuj78UvOIcy/SRpB/rgqe5wVhmH2WGy3fmn1O2BQIuvTCE4jzXPp5TSR3fp3aHIwp9bpYo118en99BdeDVAMQlbQVZnBiPyeU2l5hPnff4U4nn9/EQMw92i471PC9+TXwmKIxlHWlevbMElseJS1VRkuQs6gRdal1O2W2vAkjgfWVCVL3gnDFVmTL3m83N2l3JmjxFf3TmUOVOTh9qLSS57kanwb5suT8JDZfIej1gGKPFz/qn3UXTePP1vzAyBmYKPWQ/CyG1pUZtjlOZPmEeWxaZ78en8MSOSxxKRaInBI7KnMB0mxzTJj7y4fZDABypE3wXOAQ1pAkccXfCwyu+nKwWwZA8bAff2DlwcA20+8/Q0Qx4DxE6zvLf+873N7xlEJlrqXOU0RSEL/qEzL7vbDuNYP7+ziuGMwR6S4jAFdI8UlSCQJEkmCRJIgkSRIJAkSSYJEkiCRJEgkCRJJgkSSIJEkSCQJEkmCRJIgkSRIJAkSSUIPXQZSRFExkHGGp6fpwJaNjJuHe+0bnFUUxB3SspGhKDoSdI0kQSJJkEgSJJIEiSRBIkmQSBIkkgSJJEEiSZBIEiSSBIkkQSJJkEgSJJIEiSRhlCJbdSPYf2gFz5lgMvEQ3WpDb0nfsSZtadeNoPiZ8cbk/MQoRTbtRnBSMtvP67lyihzdqbVNNwKk//A3NvATi/WCu2B9D3GtXVJoITFdYG0XvW3NLRndEVlNgq8YuMc6rTkUItPVGwIAcF9QV6+XnfGLTFf43zIG4CKsLbvMz8hFRvBmS8Qw8JOPuz0agVGLTLFynhEAcMM17q3ydZGRimzQjeDOGKHIht0I7ozRZWO16UYApIi8d3zu/m8TBIhhYNx51nLi8QW/i5MLY6XvqaV2tO1GkHftqXvxTNeN7ogU1YzwGimqkEgSJJIEiSRBIkmQSBIkkgSJJEEiSZBIEiSSBIkkYZQilTJQQd+PX9qilIFqRilSKQNlRndqVcpANUoZIGF0R2Q1ShmgEKmUAQaRShkAMHqRShnIGbFIpQwcM1KRShkoMkKRShmoYnQBykoZqKHvqaV2KGWgjtEdkaKaEV4jRRUSSYJEkiCRJEgkCRJJgkSSIJEkSCQJEkmCRJIgkSRIJAkSSYJEkiCRJEgkCRJJgkSSMLJsrBRRlBTem+HpadrRshHRd/RXK0K3PhKui2UjQlF0JOgaSYJEkiCRJEgkCRJJgkSSIJEkSCQJEkmCRJIgkSRIJAkSSYJEkiCRJEgkCRJJArnIFJHnwNl3I5jAcTxE37YjGCfEoR6HmnUwBu58Dmw2COIYgIGfkFWU7DdkqDv2LSIKLSSSPNiqprXEWCEVmdesK7aPOF42vki57yC9Ru6K1ZtX/CqdPqd4mAPABluiayWnyHSLDQDMHypLeM4eDUo9QkYOp8g7RCJJkEgSOEVOH7JS15ttZSvCJBsJnbZfGjmcIjFDNp75Qnk8E+EzAOjaL/V9/9MV+YSAKdxI1k0UjB3iKboI3iRr8LLvSLAJEMQA4CK0ZJ17+v4ldUoSWv+44yuMNa5vS5M9BBAfkfcF6WDn/pBIEiSSBIkkQSJJ+D++jKgxIfwOhwAAAABJRU5ErkJggg==" alt="HTML image 0" height="auto" max-width="100%"> Seguindo o nosso sistema de regras estabelecido, o número \ufeff 1001 1001 1 0 0 1 \ufeff não é primo pois é divisível por 7.

Faremos o mesmo com o número 289:

Não é divisível por dois, por ser um número ímpar; Também não é divisível por \ufeff 3 3 3 \ufeff pois \ufeff ( 2 + 8 + 9 ) = 19 (2 + 8 + 9 ) = 19 ( 2 + 8 + 9 ) = 1 9 \ufeff (x); O último algoritmo de 289 é 9 , então não é divisível por 5; Tentamos dividir \ufeff 289 / 7 : 289/7: 2 8 9 / 7 : \ufeff (não é possível, pois o resto da divisão é 2) <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAF8AAAC8CAYAAAAenHLZAAAIWklEQVR4nO2dMXKrPBeGX//zLcV2kckKxArs26TKEuTSbtLdMl0aUYbutqnSXFiBWYEnRWAv+gvABgwYEsSxb95nxk1QPPJj+SDEQWdmrbUgIvxPugM/GcoXhPIFoXxBKF8QyhfkxuWn8L0ZZp6PVLorX+Ci/DSNsPE8zGaz/OVh40fNHzaN4G88eMe2M3jeBn7U0DpvOyu33bS8r3PyL3HW9fLgj9y5/zq75HtY7GIACkpr3OOAIIgR7NYIPkLY11WpdYTNYo0ACkobhA9L4PMdz7sAu3WAj9Di1Lza9vfDEp/vz9gFaywOBsl+i/m4n/Miy0cNfd987BAEiHGP5didsh0kRlllQptU/2gVYAFlTVJtC8Dq8OxNsvalA6FGY9vi78okth+JNQoWyti+/zGYUFvU+j8WnWFnvt1jv11VR+H8Fx4VAMT4SE5/Tj6yX8jd4tLXHeE9AKAMnlbVI6snAwUgLr+xMFHWWZh6Z0fgGyfcqujFnQIQ4+1vNTCmf98QA1BF4/QTh7a3nC9xDwCHz+s4gaY+ngMA6hG/HMTBL8hP8BEDqMXA+fYPjALi3QLexkeUpoiKc4YO8Wfbp/cLZN/hB65h7EcvO8QA9G9H56ChcaqI7c0xMLGhzo+jLX7ncbp2zqge07ZfhHUZ80OrMaQvwxkm/3iybelQYqzOxSpVfAnK6prl4xcIZbUJbRiG1hidv/d1yC/62P/kP5wB8ouR0DRi7WlWoIwNi+NJmI/k819KEmqr1OkXAqWsNvmX11umK/nuR721veUnR4nNM66uznaFmZb36T2tcyTf4fSyTI8TbgrfWyA7b5YvlMpN8hmMusP5THOOZcvFyxnROwIA+mH8aV1/UvjP7qaXZS7IL4tPmsUDpyli4ywlxecBqM+Ozpv58NZB4/x/UqIXZBf1bqaXZTqXF6LNIu+IBt5fsHmvNbh7wOt2BWCFJ6MQ7AKsvQP04288LJEtL7wFiGNAmSesju87wzpQ0MX1/CFAEAOAgvkz/dJCmeyiyuH0skx7RDrF+dZXLdYmobFa1aaaSlsT1mY79ZMtlFU6/ELcHjnmF7M5l8sVJWbW3nL2Qh4WIbMY911ufD3/tqF8Qf5R+RE2nTdGyq8NIqH3vfGYf9v8oyP/NqB8QShfEMoXhPIFoXxBKF8QyhdkkHxnqYMTMKjvx3/ysfGGXgUPoO/yZ/mmt9La6nKWwtntttP9XqWNDcPQhqUb5I7vzp1T3Bbs1feM0+d1dy93kHwXqYNT0N33utjTfQxlwoGpLMPoHXbcpA5OQ3ffD/gsx570L95iBZNY7LduP8BIJ9wvpg5eI/Mt9naPXgl23+V7P5y2lJHST1cbGyaJDUuZblPcortIr/SQoRl0w/iW/O+nDk5IkmXGhaGxpuiXuiT1WuWPlDo4FdXZS/lX2flf1yh/3NTB6UmyDIquz5C3uzL5U6UOTsDFuO9W/sDZzoSpg1Mi9DDGAPkTpg6OSgrf8xqWNdJjdhrulyI5P71voGcpfgBUy1N7x9TB0lOMSrWkDibYTzKRBsqDBjilKGZPGAKARmhfsSq1jzYvKDIjs3YKSt9ng+ruAU/1C7av0i86uUsdnIYkW1s6ex6g6ZqjOGe1vcaL/0wdEYTr+YJQviCULwjlC0L5glC+IJQvCOULQvmCUL4glC8I5QtC+YJQviCULwjlC0L5glC+IJQvSOdmRydSRFE9EWSB1Wr+jWOkX/bC8cmOhrv4Xz1GmL0gCWO+IJQvCOULQvmCUL4glC8I5QtC+YJQviCULwjlC0L5glC+IJQvCOULQvmCUL4gg/deiBp2DGzcMPCqig1fKf3vOJaeQlfKaq1LT5jXdxE5313wtMHQNMVgboHhWzs2lNmr/328YsP/NgP3XuhTyTMf9U0jXGhrx2ulZ8zPa+A2Vk0r9tDJt0i8pWLDwvSTXwht2Zem2MrxcvXs6yo2LM34U81is9D4DX85vDvpmS44hDl+PSrs4hi7hYcPk2129Pn5jrddscEQARxdZM23eyShhlIxgt0a6/Uau7cD7o2BVmjZf+3n0U/+hRNl097J89Ur9nsLa/PXfo/X7RKIIban2bXRc+R3nSgjZPvE9di07iqKDV8RfeekbQXZu7f0rTSctNzpLfCFAvTZHsTZ8kJz2nd2JZsvQVTaXclmplfCsB1lk9IaTWntpu5zvGLD/zbMzxeE6/mCUL4glC8I5QtC+YJQviCULwjlC0L5glC+IJQvCOULMrL8FL43q6QInr88+LyxDsDBDfTlY0s1IRSVd6Ys03TdTLekHG0wWweADmFbi2z9LCaL+VlBMAXzRPEF08hPfTwHaEk3/LlMEnaK6nKt9RR/KBOM/CK1RIMZI1Wcy0/9ZwQAlHkC3VdxHHYibGZrBGfFHwngeuTnGWrQDxTfgEP5KfxnTi+7cCc/eslq0HJ62Yoz+UWVZf17y4zkFtzIP15UGTDitMN0QUG4ni8I5QtC+YJQviCULwjlC0L5glC+IJQvCOULQvmCUL4glC8I5QtC+YJQviCULwjlC0L5gnzj4QgWKP42X96phwWKvw2zFwRhzBeE8gWhfEEoXxDKF4TyBaF8QShfEMoXhPIFoXxBKF8QyheE8gWhfEEoXxDKF8SJ/DSNsPG8yo6CG5+FiM8Y+77ksXQTlFVaW10ucMNSrBWcyFemVhmoqJHFUk0VRpffzKmENwf/iYlPuNX6iT+dieTnlaS5m2yFSeQXm9xxu68azgPb8WT7M7PSunAsvyhmyVlOEw7lc4ZzCUfyKb4PDuSXxTPWdDF6lnKxaTVUSxGDuwe8bjnnATD2bOc06ltfLMN9hPn5gnA9XxDKF4TyBfk/nyw/9JDfjrkAAAAASUVORK5CYII=" alt="HTML image 1" height="auto" max-width="100%">

Tentando dividir \ufeff 289 / 11 289/ 11 2 8 9 / 1 1 \ufeff : (logo, descobrimos que também não é possível, pois restou 03) <img src="data:image/png;base64,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" alt="HTML image 2" height="auto" max-width="100%">

Tentando dividir 289/13: (restou 7, então não é possível) <img src="data:image/png;base64,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" alt="HTML image 3" height="auto" max-width="100%">

Tentando dividir 289/17: <img src="data:image/png;base64,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" alt="HTML image 4" height="auto" max-width="100%">

Seguindo o nosso sistema de regras estabelecido, o número 289 \ufeff 1001 1001 1 0 0 1 \ufeff não é primo pois é divisível por 17 .

Faremos o mesmo com o número 181:

Não é divisível por dois, por ser um número ímpar; Também não é divisível por \ufeff 3 3 3 \ufeff pois 1 + 8 + 1 = 10 (não é divisível por 3 ); O último algoritmo de 181 é 1 , então não é divisível por 5; Tentamos dividir 181/7: (não é possível, pois o resto da divisão é 6) <img src="data:image/png;base64,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" alt="HTML image 5" height="auto" max-width="100%">

Tentamos dividir 181/11: (não é possível, pois o resto da divisão é 5) <img src="data:image/png;base64,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" alt="HTML image 6" height="auto" max-width="100%">

Tentamos dividir 181/17: (não é possível, pois o resto da divisão é 11) <img src="data:image/png;base64,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" alt="HTML image 7" height="auto" max-width="100%">

Tentamos dividir 181/19: (não é possível, pois o resto da divisão é 10) <img src="data:image/png;base64,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" alt="HTML image 8" height="auto" max-width="100%">

Tentamos dividir 181/23: (não é possível, pois o resto da divisão é 20) <img src="data:image/png;base64,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" alt="HTML image 9" height="auto" max-width="100%">

....Notem que a partir do número primo 17, aconteceu um fato diferente, pois o divisor ficou menor que o dividendo, assim, passamos a realizar operações cada vez mais complicada e que não levam a resultado. Sendo assim 181 é primo!

Obs.: A resposta não está muito convincente para mim, especialmente pois seria necessário analisar as regras matemáticas em que não foi objetivo aqui explicar como originam-se.. Porém, seria um exercício interessante realizar uma ferramenta de software para realização deste método.. Caso conheçam outros, ficarei feliz em conhecer, naturalmente as bibliotecas possuem funções prontas para realizar essas operações.

"Aprendemos diferentes raciocínios para comprovação de conhecimento no momento da prova, estes mais tardes somados com outras bagagens podem gerar resultados promissores" JTVEIGA.

Referências:

[1] Veja mais sobre "Como reconhecer os números primos" em: https://brasilescola.uol.com.br/matematica/como-reconhecer-os-numeros-primos.htm

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