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

chmy426  May 24, 2018
 #1
avatar+971 
+2

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. 

GYanggg  May 25, 2018

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