Power and value assignment puzzle

[K Sengupta]

Substitute each capital letter in bold by a different digit from 0 to 9, such that (TAU)^.BETA when rounded off to the nearest integer is equal to PI, and the absolute difference of (TAU)^.BETA and PI is the minimum. Each of T, B and P is nonzero.

 

[i.neu]

Substitute each capital letter in bold by a different digit from 0 to 9, such that (TAU)^.BETA when rounded off to the nearest integer is equal to PI, and the absolute difference of (TAU)^.BETA and PI is the minimum. Each of T, B and P is nonzero.

I underlined a little of your post there...
Do you mean PI as in π, the ratio of a circle's circumference to it's diameter?

If so since when is Pi an integer? Is that the puzzle here?

 

[K Sengupta]

Do you mean PI as in π,...

In the current puzzle, PI is a two digit positive integer in consonance with the requisite substitution in conformity with cryptarithmetic rules and does not have any connection with п.

The relevant definition of a cryptarithm is given here.