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TopNewestNumber of months with \(29 , 30\) and \(31\) days in \(1001\) leap years.

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Wow that's quick!

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Thanks.

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amazing !

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Cool observation Sir!

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Genius!

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awesome...

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Take \(x=1\) and by Chicken McNugget there exists \(y,z\) such that \(30y+31z=366337\).

That's the most straightforward way that immediately solves the problem as far as I know.

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But Chicken McNugget didn't explicitly say that \(y,z\) are positive.

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It does; or else it would just degenerate to Bezout's Identity.

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Comment deleted Apr 15, 2015

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Note that I'm looking for positive integers \(x,y,z\) not integers \(x,y,z\).

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Comment deleted Aug 14, 2015

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x=3955;y=4078;z=4171;

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x=3955;y=4078;z=4171

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see if HCF of 29,30,31 divides 366366 completely

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Won't HCF of \(29\), \(30\) and \(31\) be \(1\)?

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