Question

Find all positive integers n < 2021 whose square ends with 444.​

Answer 1

Given :   all positive integers n < 2021

To Find : whose square ends with 444.​

Solution:

All numbers of the form (500k ± 38)²  ends with 444.

Hence Numbers whose squares ends with 444

38

538

1038

1538

(2038 > 2021) ignored

462

962

1462

1962

(2462   > 2021) ignored

There are 8 numbers < 2021 whose square ends with 444.​

38 , 462 , 538 , 962 , 1038 , 1462 , 1538 , 1962

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