Let m and n be natural numbers. Show: If m2 +2n2+1 is divisible by 3 then...

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Show that a positive integer is divisible by 3 if and only if the sum of its decimal digits is divisible by 3?
Show that a positive integer is divisible by 3 if and only if the difference of the sum of its binary digits in evennumbered positions and the sum of its binary digits in odd-numbered positions is...
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