Given N = A%B, how to find the value of A%C , where B > C. You are given value of N and C, but not of A.
Is there any way to find this?
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3This question appears to be off-topic because it is about math – Aug 03 '13 at 01:35
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This question appears to be off-topic because it is about mathematics. It would fit better on the [Mathematics](http://math.stackexchange.com/) site. – Cody Gray - on strike Aug 03 '13 at 08:33
2 Answers
7
Nope. Consider the following:
A = 19
B = 10
C = 7
==> Given 9, you should get 5.
A = 29
B = 10
C = 7
==> Given 9, you should get 1.
So given the same input, there may be multiple answers.
nneonneo
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The modulo operation is one-way: given a mod b = n, all I can say is that a comes from the set of all other integers which, modulo b, equal n.
Let's demonstrate that this is impossible in general, taking B=3, C=2.
- n = a mod 3 = 1
- => a is in the set of integers {3x + 1}
- so consider, x=1
- 4 mod 3 = 1, so that works
- 4 mod 2 = 0
- now consider x=2
- 7 mod 3 = 1, so we can't distinguish 4 from 7 knowing only n and b
- 7 mod 2 = 1
That is, given b=3 and n=1, you'd have to get two different answers without knowing a.
However, you may consider it's a special case that b and c here are coprime, and in fact are both prime. You can certainly solve this easily for some cases, such as b=4 and c=2.
BTW, further discussion on this is probably better suited to mathoverflow
