- #1
ramsey2879
- 841
- 3
I found that interdependent arithmetic sequences:
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.
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.