Same Remainder
Number Theory
Level
4
Three Positive integers 1238 , 1596 , 2491 if divide by Natural Number X the remainder is Y ( Y Not 0 ) , Find X + Y ?
The answer is 343.
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1 solution
As the remainder is fixed, the divisor must be common for the differences as well. gcd(1596 - 1238 = 358, 2491 - 1596 = 895) = 179 is the natural number X and then remainder can be found Y = 164, as 1238 = 6 x 179 + 164. Answer: X + Y = 343