Arithmetic › Decimals and repeating decimals › Decimal periods

Minimal period of a sum of decimals

University · ●●●●○ 100 pts

Positive rational numbers aa and bb are written as decimal fractions, each of which has a minimal period of 30 digits. The decimal representation of a−ba-b has a minimal period of length 15. For what smallest natural number kk can the decimal representation of a+kba+kb also have a minimal period of length 15?

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number theory