0??batuta wrote:what is the remainer of this : (13^7+14^7+15^7+16^7)/58.
the answers are:
57
1
30
0
28
When n is Odd , a^n +b^n is always divisible by a+b
In this case the sum of Numerators =58 = Denominator
need an explanation
This topic has expert replies
Source: Beat The GMAT — Problem Solving |
-
Neo2000
- Legendary Member
- Posts: 519
- Joined: Sat Jan 27, 2007 7:56 am
- Location: India
- Thanked: 31 times
When n is Odd , a^n +b^n is always divisible by a+b
In this case the sum of Numerators =58 = Denominator
It is 0.
13^7+16^7+15^7+14^7
=(13+16) (smth) + (15+14) (smth)
= (29) (smth)
which leaves
(smth)/2
smth is even, thus 0
why is smth even?, the numerator in the problem is even (sum of three odds), and odd multiple out will leave it even.
regards
13^7+16^7+15^7+14^7
=(13+16) (smth) + (15+14) (smth)
= (29) (smth)
which leaves
(smth)/2
smth is even, thus 0
why is smth even?, the numerator in the problem is even (sum of three odds), and odd multiple out will leave it even.
regards
