given a, b, c being Prime such that a,b,c are_mutually_distinct and
A1: (15 |^ 2) + 1 = (a * b) * c ; :: according to NUMBER07:def 2 :: thesis: contradiction
15 |^ 2 = 15 * 15 by WSIERP_1:1;

per cases then ( ( a * b = 1 & c = 226 ) or ( a * b = 2 & c = 113 ) or ( a * b = 113 & c = 2 ) or ( a * b = 226 & c = 1 ) ) by A1, Th35;

suppose ( a * b = 1 & c = 226 ) ; :: thesis: contradiction

hence contradiction by XPRIMES0:226; :: thesis: verum

end;

suppose ( a * b = 2 & c = 113 ) ; :: thesis: contradiction

hence contradiction by XPRIMES1:2; :: thesis: verum

end;

suppose ( a * b = 113 & c = 2 ) ; :: thesis: contradiction

hence contradiction by XPRIMES1:113; :: thesis: verum

end;

suppose ( a * b = 226 & c = 1 ) ; :: thesis: contradiction

hence contradiction by XPRIMES0:1; :: thesis: verum

end;

end;