+0

# Prime Number

+2
80
1
+41

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

chmy426  May 24, 2018
#1
+901
+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