Even?!! It doesn't matter
Number Theory
Level
3
The number 'n' is a constant such that the equation 2a + 3b = 4n has 20 solutions in positive integers. In how many of those solutions is 'b' also even?
The answer is 20.
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1 solution
4n can never be expressed as x(any even no.) + 3(2m+1)
whatever be the value of x; if 3 will be multiplied by an odd natural no., it will be impossible to express as multiple of n by adding any even natural no.
Thus, b has to be even in all the cases!