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Number of ways of selecting two integers 'a' and 'b' from the set{1,2,3,4,.....5n}, n€N so that a4-b4 is divisible by5?
A)17n2+5n/2 B)15n2-17n/2 C)17n2-5n/2 D)15n2+17n/2
Dear siri
give set {1,2,3,4,.....5n}
case 1: when intiger a,b, are prime to 5. then (a4-1) and (b4-1) will be divisible by 5
a4 -b4 =(a4-1)- (b4 -1)
total number of selecting rhe a,b = 4n(4n-1)/2
case 2 : when a,b are multiple of 5
total number of selecting rhe a,b = n(n-1)/2
so total = 4n(4n-1)/2 + n(n-1)/2
=17n2-5n/2
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