Math Is Fun Forum

  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

#1 2007-10-07 10:33:46

Dave57
Guest

Congruence question

Hey everyone. I have a question about a congruence problem. I guess I'm just unsure about how to approach it:

If p is a prime number and if a is not congruent to 0 (mod p), then Fermat's Little Theorem tells us that a^(p-1)≡ 1 (mod p).

The congruence 7^1734250 ≡ 1660565 (mod 1734251) is true. Can you conclude that 1734251 is a composite number?

#2 2007-10-08 04:32:34

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

Re: Congruence question

Can you conclude that 1734251 is a composite number?

I believe that is supposed to say "prime" number.  And the answer is obviously (this is a psychology question, not math) no.  The reason for is that the converse of a statement does not always hold.  One of the smallest examples I know of is:

2^340 = 1 (mod 341)

But 341 is not prime.


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

Offline

Board footer

Powered by FluxBB