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Part of 1991 Tournament Of Towns

Problems(1)

TOT 287 1991 Spring A J3 numbers ending with digit 5

Source:

6/9/2024
We are looking for numbers ending with the digit 55 such that in their decimal expansion each digit beginning with the second digit is no less than the previous one. Moreover the squares of these numbers must also possess the same property. (a) Find four such numbers. (b) Prove that there are infinitely many.
(A. Andjans, Riga)
number theoryDigits