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What is the smallest prime number that divides exactly into 312+513+714+1115?

 May 24, 2018

The smallest prime number is 2. 


We can check if \(3^{12}+5^{13}+7^{14}+11^{15}\equiv0\pmod2\)


Since the product of any amount of odd numbers is odd:


3 is odd

32 is odd

3is odd



We know that the expression is:


odd + odd + odd + odd = even 


Since the expression is even, it must be divisible by 2. 

 May 25, 2018

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