The remainder when 7^89761 is divided by 15 is?

Question

anonymous · Answer

@experimentX @phi @satellite73 @saifoo.khan @apoorvk @yash2651995

saifoo.khan · Answer

calc?

anonymous · Answer

Nop........there should be some otherway! calculating is impossible

saifoo.khan · Answer

So we have to solve with calculation?

experimentx · Answer

try to find some cylic pattern

lgbasallote · Answer

must have something to do with the exponent

anonymous · Answer

http://openstudy.com/study#/updates/4fc8fe7ee4b0c6963ad353fd

anonymous · Answer

@satellite73  i got the pattern but the answer should be 7 there it has written1!!

anonymous · Answer

@phi

experimentx · Answer

lol ... i remember that
yes i guess it should be 7

experimentx · Answer

http://www.wolframalpha.com/input/?i=7%5E89761+mod+15

btaylor · Answer

There is a trend when dividing powers of 7 by 15.
7^0/15 = R1
7^1/15 = R7
7^2/15 = R4
7^3/15 = R13
7^4/15 = R1
7^5/15 = R7
7^6/15 = R4
7^7/15 = R13
So 7^(4n) will have a remainder of 1, 7^(4n+1) will have a remainder 7, and so on. 
89761 is a 4n+1 type.

anonymous · Answer

@experimentX  how 7 i too got 1 plz  help

experimentx · Answer

7^(89761 mod 4) mod 15
89761 mod 4 = 1
so, 7^1 mod 15 = 7

anonymous · Answer

@experimentX  is that mod is absolute value

experimentx · Answer

no ... modulus
remainder when you divide some number by some number

experimentx · Answer

try experimenting http://www.wolframalpha.com/input/?i=7+mod+5

anonymous · Answer

can u detaily write it becoz it is an imp step i am confused

experimentx · Answer

Oh sorry ... it's called modulo ,,, or so

anonymous · Answer

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