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6

Part of 2013 Argentina National Olympiad

Problems(1)

Pretty numbers

Source: Argentine National Olympiad 2013, Level 3, Problem 6

8/31/2014
A positive integer nn is called pretty if there exists two divisors d1,d2d_1,d_2 of nn (1≤d1,d2≤n)(1\leq d_1,d_2\leq n) such that d2−d1=dd_2-d_1=d for each divisor dd of nn (where 1<d<n1<d<n). Find the smallest pretty number larger than 401401 that is a multiple of 401401.
number theory unsolvednumber theory