I found that interdependent arithmetic sequences:(adsbygoogle = window.adsbygoogle || []).push({});

A*n + B, C*n + D, and E*n +F solving the

formula T(A*n+B)=(C*n+D)*(E*n+F), for all integer n can be

generated by the equations

A=(2m+1)*(2m+2)

B=(2m+2)*2m

C=+/- (2m+2)*(m+1)

D=+/- (2m+1)*(m+1)

E=+/- (2m+1)*(2m+1)

F=+/- (2m+1)*2m

I tried to find an example not generated by these formulas but could not. I believe that this finding has many implications with congruences.

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# Triangular numbers, T(An +B), that equal (Cn+D)*(En+F) for all n

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