= 75880433**87109376**

= 1661682**12890625**

A general form: numbers whose squares end with the same…

… 2 digits:

… 3 digits:

… 4 digits:

… 5 digits:

… 6 digits:

… 7 digits:

… 8 digits:

… 9 digits:

… 10 digits:

… 11 digits:

… 12 digits:

… 13 digits:

… 14 digits:

… 15 digits:

… 16 digits:

… 17 digits:

… 18 digits:

… 19 digits:

… 20 digits:

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Here is a list of numbers up to 20 digits

25^2 = 625

76^2 = 5776

625^2 = 390625

9376^2 = 87909376

109376^2 = 11963109376

890625^2 = 793212890625

12890625^2 = 166168212890625

87109376^2 = 7588043387109376

1787109376^2 = 3193759921787109376

8212890625^2 = 67451572418212890625

81787109376^2 = 6689131260081787109376

918212890625^2 = 843114912509918212890625

40081787109376^2 = 1606549657881340081787109376

59918212890625^2 = 3590192236006259918212890625

3740081787109376^2 = 13988211774267263740081787109376

6259918212890625^2 = 39186576032079756259918212890625

256259918212890625^2 = 65669145682477392256259918212890625

743740081787109376^2 = 553149309256696143743740081787109376

7743740081787109376^2 = 59965510454276227407743740081787109376

92256259918212890625^2 = 8511217494096854352392256259918212890625

2607743740081787109376^2 = 6800327413935747244982607743740081787109376

7392256259918212890625^2 = 54645452612300005057477392256259918212890625

Paul.

I posted a general form up to 10 digits

I’ve added more

Here’s my MMa code for the list above, its based on this

Mod[3n^2 – 2n^3,10^(2k)] where n=5 or 6 and k=1, the result is a new n and inc k to 2 etc

Paul.