Finding perfect squares

Number Theory Level 2

Find the number of perfect squares in the sequence below! 11 , 211 , 2211 , 22211 , 222211 , … 11, 211, 2211, 22211, 222211, \dots

1 Infinite many 0 Finite many, and more than 1

Áron Bán-Szabó by Áron Bán-Szabó , 17, Hungary

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2 solutions

Áron Bán-Szabó
Aug 28, 2017

Each number makes 3 3 remainder, when it is divided by 4 4 . However a perfect square makes 0 0 or 1 1 remainder, when it is divided by 4 4 .

4 Helpful 0 Interesting 0 Brilliant 0 Confused
Utkarsh Kumar
Aug 28, 2017

Each number in the sequence is certainly divisible by 11 but not by 121. So they can never be perfect squares

0 Helpful 0 Interesting 0 Brilliant 0 Confused

No. 211 is not divisible by 11. Neither is 22211, or any number with an odd number of 2's.

Siva Budaraju - 3 years, 9 months ago

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