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anonymous
 one year ago
How do I check 12321 ≡ 111 (mod 3) is true without applying the definition?
anonymous
 one year ago
How do I check 12321 ≡ 111 (mod 3) is true without applying the definition?

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mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1as far as i see both are divisible \(3\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yeah, but that's more like by inspection. I need to use properties of congruences

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.112321 and 111 are divisible by 3 is sufficient

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1\(12321\equiv 0 \pmod {3}\) and \(111\equiv 0\pmod{3}\) \(\implies 12321 \equiv 111\pmod{3}\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0by transitive property?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1Yep \(a\equiv c\pmod{n}\) and \(c\equiv b\pmod{n}\) \(\implies a\equiv b\pmod{n}\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ah yes. I guess this was too easy. Let me pick a different problem. 12345678987654321 ≡ 0 (mod 12345678) ^^

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0It's according to wolfram alpha, But 12345678987654321 ≡ 0 (mod 12345679) is true though

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0it's *false* according...

anonymous
 one year ago
Best ResponseYou've already chosen the best response.012345678987654321 / 12345679 = 999,999,999

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0This problem seems challenging but it's in the section where it covers algebraic properties of congruences (addition,subtract and such...). I'm just assuming the exercise is meant for us to apply those properties but it doesn't seem like it.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Maybe the exercises are meant to check the readers' understanding of the definition. Who knows.
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