Possible values of n*n mod 7
If a number n leaves a reminder "k" when divided by 7 what are the possible values of n*n mod 7. Assume that k is not equal to 0.
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1 solution
Two issues:
- Nothing in the problem statement implies k = 0 , and
- 2 2 = 4 = 3 .
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I have stated that k not equal to 0, the second point is not clear. If k = 2 then k*k when divided by 7 will leave a reminder of 3.
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With your edit, yes, I agree that k = 0 now.
Okay... when k = 2 , we have k ⋅ k = 4 . Are you really saying 4 , when divided by 7 , will leave a remainder of 3 ?
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@Brian Moehring – Oops it will just leave a reminder of 4. The answer changes to 1,2 and 4. Request the Brilliant staff to kindly modify the correct answer choice to 1,2 and 4
There is no answer option showing your solution 1,2,4 . Therefore, the answer should be None of the above .
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Have requested the admin staff to modify the answer choice.
Let the number "n" be written as 7r + k ; So n n = 49 r r + 14 r k + k k . Dividing n n by 7 , the first two terms are divisible by 7 so it is enough to investigate the term k k/7 in order to determine the possible values of n n mod 7.. K can be 1, 2,3,4,5, or 6 (non zero as per the question), so k k /7 can leave a reminder of 1,4,2,2,4,1 , rearraning , the possible values are 1,2 and 4.