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The set of values of xx satisfying 26≡5(modx)26 \equiv 5 \pmod{x} is _______.

Solution

✅ Correct Option: 4

26≡5(modx)26 \equiv 5 \pmod{x} requires x∣(26−5)=21x | (26 - 5) = 21. Divisors of 21 are 1,3,7,211, 3, 7, 21. Excluding the trivial x=1x = 1 leaves {3,7,21}\{3, 7, 21\}. Check x=3x = 3: 26=8(3)+226 = 8(3) + 2 and 5=1(3)+25 = 1(3) + 2, both have remainder 2, so they are congruent mod 3. So {3,7,21}\{3, 7, 21\}.

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