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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