+63 What is the smallest prime number that divides exactly into 312+513+714+1115?
+981 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
33 is odd
...
We know that the expression is:
odd + odd + odd + odd = even
Since the expression is even, it must be divisible by 2.
