N is the greatest number that divides 2045, 3417 and 4887 leaving the same remainder each time. What is that common remainder?

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Accepted Answer

85. N divides the differences 3417 − 2045 = 1372 and 4887 − 3417 = 1470. 1372 = 2^2 × 7^3 and 1470 = 2 × 3 × 5 × 7^2, so N = 2 × 7^2 = 98. 2045 = 20 × 98 + 85, so the remainder is 85 (check: 3417 = 34 × 98 + 85).

N is the greatest number that divides 2045, 3417 and 4887 leaving the same remainder each time. What is that common remainder?

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