It is given that,

Note:

I. Sum of first n natural numbers, 1 + 2 +3+…n,

II. Sum of squares of first n natural numbers, 1² + 2² + 3²+….n²,

From the above identities,

n² + n = 420

n² + n -420 = 0

(n – 20) (n + 21) = 0

n = 20 or -21

Since, n is the number of integers, n = 20

So,