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I am on the love it team. I did not need spreadsheet or even calculator. Just a list of primes and a list of square numbers and asking google to factorise a few numbers at the end.
No need for brute force, just eliminating options by steady perseverance and a bit of sudoku. The fact that all the answers were different proved quite helpful in the middle.

Byron, the maths puzzles aren't my forte, so I try to re-do them. They often look simpler in the rear-view mirror, but what doesn't? All clues here were solvable with logic, but it took me hours to work out how! 7d was a good example. I sometimes try other maths puzzles, but they often involve more brute force - processing lists of numbers - rather than, as with The Listener, scratching about in the darkness before laughing at how simple the answer actually is.

I've been doing the Listener Maths crossword for years and have been able to find a logical path every time without trial and error. I didn't solve 7 down because there are too many possibilities in other cells in its column and similarly in its row. In total there were all 9 possible numbers in other squares that hadn't been resolved, so Sudoku rules were not going to eliminate anything. The consensus view on this website is that trial and error had to be applied. I will return to it again, but feel I reached an impasse on Sunday when I started it with only 9 squares filled very quickly, then lots of multiple solutions in other squares.

Managed to solve 7dn after re-visiting the puzzle. Now have half the grid finished with single values, quite a number with 2 values and some with 4 values. I had neglected the power of Sudoku earlier, particularly with regard to the null hypothesis, but I am now left with no other recourse than to make assumptions about those squares with anomalous values. The diagonals at this stage have too many possible solutions to be of any value! I'm not sure I have the energy to continue by saying 'Let's assume .... and also assume .... and see where that takes us. One assumption yes, but not two because that has four combinations!

Phew! - got there in the end and the final with the diagonals was brilliant, if not tense! I think my earlier issues were due to my lack of Sudoku skills. What a puzzle though, but definitely worth persevering with. Many thanks to IOA and all the gentle hints from the other solvers o this forum!

Glad you got there, Byron. Always hard to do more than hint with the maths puzzles. Agree with you about the diagonals. Impressed as a I was, it still took my snail brain a long time to work out how to use them!

Wow, after a long time on and off with this I finally got it. No brute force needed just a lot of elimination. Amazing how the thing leads you through and never gives up too much right until the end. I'm amazed at how a puzzle can be constructed such that only a little can be unlocked at any time. The diagonal rows factorisation was fascinating. Thank you IOA if you're reading...

And (as i eventually found out) there was no need for trial and error... When certain clues were considered together, it was then clear that there was then only 1 possibility for the particular clue which had 2 possibilities (if that makes sense). I don't think it would be fair if trial and error was the only way to complete it.