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Tems11 [23]
2 years ago
7

Find the greatest number that divides451, 328 and 673 leaving 1, 4 and 1,respectively as remainders.

Mathematics
1 answer:
Vesna [10]2 years ago
4 0

You're looking for the largest number <em>x</em> such that

<em>x</em> ≡ 1 (mod 451)

<em>x</em> ≡ 4 (mod 328)

<em>x</em> ≡ 1 (mod 673)

Recall that

<em>x</em> ≡ <em>a</em> (mod <em>m</em>)

<em>x</em> ≡ <em>b</em> (mod <em>n</em>)

is solvable only when <em>a</em> ≡ <em>b</em> (mod gcd(<em>m</em>, <em>n</em>)). But this is not the case here; with <em>m</em> = 451 and <em>n</em> = 328, we have gcd(<em>m</em>, <em>n</em>) = 41, and clearly

1 ≡ 4 (mod 41)

is not true.

So there is no such number.

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