Hello,

Can someone help me on questions below please ?

Express each of the following in First Order Peano Arithmetic (FOPA), using carefully defined abbreviations:

(i) v1 and v2 differ by a prime. (Careful! Maybe v1 < v2; maybe not.)

(ii) v1 and v2 are equal modulo v3 (i.e., v1 and v2 differ by a multiple of v3).

(iii) No number equal to 7 modulo 8 can be expressed as the sum of three squares.