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Find smallest N for 5-and-21 sums

SchonfeldData Scientist · Online Assessment
MediumData ScientistOnline AssessmentCoding & Algorithms

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This question evaluates understanding of integer linear combinations and elementary number theory, framed as a Frobenius coin problem that examines representability using non-negative multiples of 5 and 21.

You are given two positive integers: 5 and 21. We say a positive integer x is representable if it can be written in the form

[ x = 5a + 21b ]

for some non‑negative integers a and b (i.e., using any number of 5s and 21s, order does not matter).

For example, 99 is representable because:

  • 99 = 21 + 21 + 21 + 21 + 5 + 5 + 5.

Find the smallest integer N such that every integer greater than or equal to N is representable.

Output this minimal value of N.