Question

find me I am a 4 digit number I have no zeros I am a square number sum of all my digits is a square number some of my first 2 digits is a square number some of my last two digit is a square number​

Answer 1

Given :  4 digit number

no zeros

Square number

Sum of first 2 digits is a square number

Sum of last 2 digits is a square number

Sum of all digits is a square number

To Find : Number

Solution:

Sum of first 2 digit is square

sum of last two digit is square

sum of all 4 digits is square

Hence possible combination is

9 + 16  = 25   or  16 + 9  =  25

16  = 79 , 97 , 88

Unit digit must be   1 , 4 , 5 , 6  , 9  

9 + 16 = 25 case can have

AB79

A+B  = 9

1879 , 2779 , 3679 , 4579 , 5479 , 6379 , 7279, 8179

16 + 9  = 25

7981  , 7954 , 7945 , 7936

9781 , 9754 , 9745 , 9736

8881 , 8854 , 8845 , 8836

8836  = 94²

This is only possible number

Hence 8836 is correct answer

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Answer 2

Answer:

1681

Step-by-step explanation:

Yeah...That's a nice number one can has heard of. However I don't have a formal proof for the fact that this is the only 4- digit number, but since they are limited, one can check.