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let n be a natural number such that the division n¡5 leaves a remainder 4 and the division n¡2 leaves a remainder 1 what must be the unit digit of n?

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  1. n=2k+1, so clearly n must be odd.

    Now, it is also 5k+4, so k must be odd since otherwise 5k is even, and so is n.

    Any odd multiple of 5 ends in 5, so n must end in 9.

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