M4maths Previous Puzzles

26 Sep 2012 number

4^125 + 125^4 is

OPtion

1) prime
2) composite even
3) composite odd
4) not possible to decide
5) none of these

Solution

4^125 + 125^4
= (2^125)^2 + (125^2)^2
= (2^125)^2 + (125^2)^2 + 2*2^125*125^2 - 2*2^125*125^2
= (2^125+125^2)^2 - 2^126*125^2
= (2^125+125^2)^2 - (2^63*125)^2
now use a^2-b^2 = (a+b)(a-b) to prove the number composite.

Correct Option: 3 Best Solution (3)