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Number Theory Level 2

Let $a, b,$ and $c$ be primes such that $a + b + c = 100$ and $c - b$ = 36.

What are the values of $a, b,$ and $c$ ? Give your answer as the concatenation of $a, b,$ and $c.$

For instance, if $a = 30, b = 20, c = 10$ , then your answer will be 302010.

The answer is 23167.

1 solution

Nelson Mandela
Dec 30, 2014

sum of 3 numbers is 100 implies that one number is even so a= only even prime=2. now, c+b=98 c-b=36 adding the 2 equations we have 2c =134 thus,c=67 that implies b=31

thus the solution is 23167.

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The answer is 23167.

1 solution

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