Question 209624
So, we've got two squares with whole-number sides, and the difference between their areas is 29.

We know that the difference of two squares is {{{x^2 - y^2 = (x-y)(x+y)}}}, so we need to figure out what multiplies to make 29... and we know 29 is prime, so the factors must be 1 and 29.

Since x and y are both positive, they have to add up to more than their difference, so we get

1) x + y = 29
2) x - y =  1

We can solve that several ways, all of which give us x = 15 (this year's crop) and y = 14 (last year's). This year there are {{{x^2 = 15 * 15 = 225}}} trees; last year there were 196.