A woman, under sixty, told me, that the square of her age equals the sum of the squares of her children's ages.
How old is she , given that the children's ages form an arithmetic series of nine integers?
(In reply to possible solution
You say: "...a=2, n=3, giving Mum the age of 48.. In fact any multiple of 3 will do, but the next one, n=6, makes Mum an aged crone with an infant in arms ..." etc
This remark of yours ,rephrased as "any multiple of the series (like a=4, n=6 or a=6, n=9 etc)will do" justifies staying with one solution even without the "under sixty" constraint.
I did not include this constraint in my original puzzle, but the post got stuck in the queue due to discussion whether the solution is unique or there might be others like 4.10,16..+mother of 96 etc or even 6, 15, 24 + mother of 144.
To avoid further counter-productive claims like whether adopting children gains the "aged crone" a title of Mother, I reluctantly added the above 2-word disclaimer.