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anonymous
 4 years ago
The positive n integer is not divisible by 7 . The remainder when n is divided by 7 and the remainder when n^2 is divided by 7 are each equal to k . What is k? Help with solving a problem like this please!
anonymous
 4 years ago
The positive n integer is not divisible by 7 . The remainder when n is divided by 7 and the remainder when n^2 is divided by 7 are each equal to k . What is k? Help with solving a problem like this please!

This Question is Closed

bahrom7893
 4 years ago
Best ResponseYou've already chosen the best response.3Let's try this the old fashioned long division way..

bahrom7893
 4 years ago
Best ResponseYou've already chosen the best response.3dw:1328418115277:dw

bahrom7893
 4 years ago
Best ResponseYou've already chosen the best response.3dw:1328418167975:dw

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0dw:1328418236084:dw

bahrom7893
 4 years ago
Best ResponseYou've already chosen the best response.3sorry those are my random thoughts

bahrom7893
 4 years ago
Best ResponseYou've already chosen the best response.3don't have scrap paper on me

bahrom7893
 4 years ago
Best ResponseYou've already chosen the best response.3just gotta get the k in terms of n and 7.. hold on

bahrom7893
 4 years ago
Best ResponseYou've already chosen the best response.3im still thinkin btw haha

bahrom7893
 4 years ago
Best ResponseYou've already chosen the best response.3i think it's 1, just gotta prove it

bahrom7893
 4 years ago
Best ResponseYou've already chosen the best response.3okay, i think i got it: Suppose n=7a+k and n^2=7b+k

bahrom7893
 4 years ago
Best ResponseYou've already chosen the best response.3subtracting the two equations: nn^2 = (7a+k)  (7b+k) or nn^2 = 7a7b = 7(ab)

bahrom7893
 4 years ago
Best ResponseYou've already chosen the best response.3or n(n1)=7(ab). Now this means that either n is divisible by 7 or n1 is divisible by 7.

bahrom7893
 4 years ago
Best ResponseYou've already chosen the best response.3Let ab be some integer, so n(n1) = 7i. As I've said either n is divisible by 7 or n1 is divisible by 7 (whichever one's divisible by 7 would mean that the other one's divisible by i).

bahrom7893
 4 years ago
Best ResponseYou've already chosen the best response.3We know that n is not divisible by 7 (given), that means n1 must be divisible by 7

bahrom7893
 4 years ago
Best ResponseYou've already chosen the best response.3Thus, if n1 is some multiple of 7, n1=7*x; or n = 7*x+1

bahrom7893
 4 years ago
Best ResponseYou've already chosen the best response.3which makes k = 1. Actually let's test this.

bahrom7893
 4 years ago
Best ResponseYou've already chosen the best response.38/7 has remainder 1, so does 64/7

Directrix
 4 years ago
Best ResponseYou've already chosen the best response.0Try 30 and then 30^2 and test for equal remainders.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0n : 7 =x+k n^2 :7=y+k k=? n :7 =x+k  n=x*7 +k ((x*7)+k)^2 :7=y+k 49x^2 +14kx +k^2 =7y+7k 14kx +k^2 7k =7y49x^2 k^2 +7k(2x1) =7y49x^2 k^2 +7(2x1)k 7y+49x^2 =0 k^2 +7(2x1)k 7(y7x^2) =0  so now just you need to solve this quadratic equation for k_1 and k_2 ....  hope that is understandably !!! good luck bye
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