The greatest value of x satisfying 21 equiv 3 | vedclass

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(C) The condition $a \equiv b \pmod{x}$ implies that $x$ is a divisor of $(a - b)$.For the first congruence: $21 \equiv 385 \pmod{x}$,we have $x$ divi

Vedclass · Accepted Answer

$28$

Vedclass · Answer

(C) The condition $a \equiv b \pmod{x}$ implies that $x$ is a divisor of $(a - b)$.For the first congruence: $21 \equiv 385 \pmod{x}$,we have $x$ divides $(385 - 21) = 364$.The divisors of $364$ are $1, 2, 4, 7, 13, 14, 26, 28, 52, 91, 182, 364$.For the second congruence: $587 \equiv 167 \pmod{x}$,we have $x$ divides $(587 - 167) = 420$.The divisors of $420$ are $1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420$.The greatest common divisor of $364$ and $420$ is $gcd(364, 420) = 28$.Thus,the greatest value of $x$ is $28$.

The greatest value of $x$ satisfying $21 \equiv 385 \pmod{x}$ and $587 \equiv 167 \pmod{x}$ is

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