Finding the totient functionlike function for an irrational number like (a+b*sqrt(5)) where a and b are whole numbers mod M where M is a whole number.

38 Views Asked by At

I need to find if a value $T$ exists for irrational number of the form

$(a+b\cdot \sqrt{5})$ such that $(a+b\cdot \sqrt{5})^T = 1 \pmod M$.

Also ,is it possible to find out upper bound for T .