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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?
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..."
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