mathematical induction

oh an easy one
We will prove it using first principle of mathematical induction (FPI)

Let p (n) = n⁵5 + n³3 + 7n15......................1

p (1) = 1⁵5 + 1³3 + 715 = 1 which is an integer . ...............2
Now lets suppose p (n) is true for every natural number ' n' . We
will show that it is also true for for (n+1)
p (n+1) = (n+1)⁵5 + (n+1)³3 + 7(n+1)15
≡ n⁵+ 5n⁴ + 10n³+ 10n² + 5n + 15 + n³+ 3n²+ 3n+ 13 + 7n+715
≡ n⁵5 + 5n⁴5+10n³5+10n²5+5n5+15+ n³3 + 3n²3+3n3+13+7n15+715
≡ n⁵5 + n³3 + 7n15 + n⁴ + 2n³ + 2n² + n² + n + 1⁵5 + 1³3 + 715

From 1 and 2 and also because n is a natural number

n⁵5 + n³3 + 7n15 is always an integer :)

Thank you.I only wanted the answer using the first principle.Didnt mention it :D