For 10 points, name these numbers found by multiplying integers by themselves, such as 4, 9, and 16.
Exactly three of these numbers appear in the Fibonacci sequence. Lagrange proved that all positive integers can be written as sums of four of them. They have an odd number of positive divisors, and the nth one equals the sum of the (*) first n odd natural numbers. The prime factorizations of these numbers have all even exponents. For 10 points, name these numbers found by multiplying integers by themselves, such as 4, 9, and 16.
Exactly three of these numbers appear in the Fibonacci sequence.
perfect squares (accept square numbers; do not accept "square roots")