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a) How many positive integers N from 1 to 5000 satisfy the congruence N equiv 5 (mod 12)?

b) How many positive integers N from 1 to 5000 satisfy the congruence N equiv 11 (mod 13)?

c) How many positive integers N from 1 to 5000 satisfy both equations above?

Thanks guys!

 Dec 18, 2020
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By computer program

for (1 <= n <= 5000) {

  if n % 12 == 5 then a = a + 1

  if n % 13 == 1 then b = b + 1

  if n % 12 == 5 and n % 13 == 1 then c = c + 1

}

 

(a) The answer is a = 401.

 

(b) The answer is b = 374.

 

(c) The answer is c = 28.

 Dec 28, 2020

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