+0

# Prime Number

+2
161
1
+53

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

May 24, 2018

#1
+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.

May 25, 2018