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What is the modular representation of an integer using a set of primes?

More specifically, a problem on my homework asks to convert 49 to a modular representation using primes 7,11,13,17.

Would appreciate a general solution.

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Perhaps they're just asking for $49\pmod p$? It certainly doesn't seem like standard terminology to me. – EuYu Oct 14 '12 at 3:04
Are you suggesting there are multiple representations of 49, one for each prime? – James Oct 14 '12 at 3:20
Well, yes. It seems like a highly ambiguous problem to me in either case, but $49$ has a representation modulo $p$ for each $p$. So this is certainly one possible interpretation. – EuYu Oct 14 '12 at 3:21
Find the remainders when you divide $49$ by the various primes, string them in a row: it is a quadruple that starts with $0, 5$. – André Nicolas Oct 14 '12 at 5:22
up vote 0 down vote accepted

Your textbook surely states what they mean by the phrase.

But to take a guess, they're probably referring to a "residue number system", where you represent not-too-large integers as a sequence of residue classes modulo a set of moduli (usually primes).

(to do the reverse conversion, from the residue number system to decimal (or other representations) typically involves the Chinese Remainder Theorem)

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The thing is, our problem sets have been known to not follow our text's conventions, which is why I wondered if this community could provide some clarification. I have emailed the professor and will update this question. – James Oct 14 '12 at 3:46

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