Define a number K such that it is the sum of the squares of the first M natural numbers.(i.e. K = 1² +2²+...+ M^2) where M< 55. How many values of M exist such that K is divisible by 4?
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hi please mention the class also so that we can answer easily
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12
Step-by-step explanation:
the sum of the squares of first n natural number is n(n+1)(2n+1)/6
for this number to be divisible by 4 the product of n(n+1)(2n+1) needs to be multiple of 8 . out of the 2 n or n+1 only one can be even , 2n+1 will always be odd.
thus either of n or n+1 should be multiple of 8
like n=7,8,15 and so on
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