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5

Part of 2018 Costa Rica - Final Round

Problems(1)

M = (a + b)^2-ab is a multiple of 5 for even a,b

Source: OLCOMA Costa Rica National Olympiad, Final Round, 2018 3.5

9/20/2021
Let aa and b b be even numbers, such that M=(a+b)2āˆ’abM = (a + b)^2-ab is a multiple of 55. Consider the following statements: I) The unit digits of a3a^3 and b3b^3 are different. II) MM is divisible by 100100. Please indicate which of the above statements are true with certainty.
number theorydivisibledivides