Palindrome 97779

 
 
 
97779   is a palindrome,   and

97779 \; - \; (9\times 7\times 7\times 7\times 9) \; = \; 69996    is a palindrome

 

There are four pandigital perfect squares whose square roots contain only odd digits.
One of them is :

97779^2 \; = \; 9560732841    is a pandigital square

 
 

Paul found:

35337^2 \; = \; 1248703569
35757^2 \; = \; 1278563049
75759^2 \; = \; 5739426081

 

Note that:

1 \; + \; \sum_{k=1}^n \, {p_k}^2 \; = \; 1 + (p_1)^2 + (p_2)^2 + (p_3)^2 + ... + (p_n)^2

35337 \; = \; 1 \; + \; (2^2 + 3^2 + 5^2 + 7^2 + 11^2 + ... + 73^2)

 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

math grad - Interest: Number theory
This entry was posted in Number Puzzles and tagged . Bookmark the permalink.

2 Responses to Palindrome 97779

  1. paul says:

    These would be them

    35337^2 = 1248703569
    35757^2 = 1278563049
    75759^2 = 5739426081

    Paul.

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