Your class must be taking computer programming. This is a job for a simple computer program to figure out. I wrote a short code to search up to 10,000,000 numbers and came up with these:
n= 3^2 + 4^2 = 25
n= 20^2 + 21^2 = 841
n= 119^2 + 120^2 = 28,561
n= 696^2 + 697^2 = 970,225
n= 4,059^2 + 4,060^2 = 32,959,081
n= 23,660^2 + 23,661^2 = 1,119,638,521
n= 137,903^2 + 137,904^2 = 38,034,750,625
n= 803,760^2 + 803,761^2 = 1,292,061,882,721
n= 4,684,659^2 + 4,684,660^2 = 43,892,069,261,881