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need an explanation

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by batuta » Tue May 08, 2007 3:14 am
what is the remainer of this : (13^7+14^7+15^7+16^7)/58.
the answers are:
57
1
30
0
28
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Re: need an explanation

by Neo2000 » Tue May 08, 2007 4:02 am
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
0??

When n is Odd , a^n +b^n is always divisible by a+b

In this case the sum of Numerators =58 = Denominator
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by f2001290 » Tue May 08, 2007 6:10 am
Neo

I think you gave a shot at CAT :)
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by chitoshia » Tue May 08, 2007 6:37 am
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
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by Neo2000 » Tue May 08, 2007 8:32 am
f2001290 wrote:Neo

I think you gave a shot at CAT :)
Guilty!

Guilty!

Guilty!

:lol:
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