Question Number 149323 by naka3546 last updated on 04/Aug/21

How many ordered pairs (a,b) with b < a < 100 , a,b ∈ N such that (a/b) both ((a+1)/(b+1)) are integers .

Answered by Olaf_Thorendsen last updated on 05/Aug/21

N = Σ_(b=1) ^(98) Σ_(a=b+1) ^(99) ⌊((⌊(a/b)⌋)/(a/b))×((⌊((a+1)/(b+1))⌋)/((a+1)/(b+1)))⌋ N = 85

Commented bynaka3546 last updated on 05/Aug/21

thank you, sir.

Answered by Olaf_Thorendsen last updated on 05/Aug/21