Statement I:
2513+313 → divisible by (25+3)
2013+813 → divisible by (20+8)
∴ divisible by 7. TRUE
Statement II:
For (7+43)25, let α=7+43 and β=7−43 (conjugate).
Then αβ=1 and α+β=14.
Since 0<β<1, we have α25+β25 is an integer.
The fractional part of α25 is 1−β25, making the integral part odd. TRUE.
Both Statement I and Statement II are true.