How-many-ordered-pairs-a-b-with-b-lt-a-lt-100-a-b-N-such-that-a-b-both-a-1-b-1-are-integers-

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

H o w m a n y o r d e r e d p a i r s (a, b) w i t h b < a < 100, a, b \in N s u c h t h a t \frac{a}{b} b o t h \frac{a + 1}{b + 1} a r e i n t e g e r s .

Answered by Olaf_Thorendsen last updated on 05/Aug/21

N = \underset{b = 1}{\sum^{98}} \underset{a = b + 1}{\sum^{99}} ⌊ \frac{⌊ \frac{a}{b} ⌋}{\frac{a}{b}} \times \frac{⌊ \frac{a + 1}{b + 1} ⌋}{\frac{a + 1}{b + 1}} ⌋

N = 85

Commented by naka3546 last updated on 05/Aug/21

t h a n k y o u, s i r .

Answered by Olaf_Thorendsen last updated on 05/Aug/21