[seqfan] Prepend k to square to get another square!

[zak seidov]

Dear seqfans,

1. Prepend k (from the list) to square 
to get another square!

k= 
25,26,37,38,40,41,43,59,61,62,64,65,97,100,101,103,124,125,127,157,158,160,190,191,193,194,196,197,199,200

1a. Or prove that it's impossible for such k's. 

2. Find more such k's!
3. Any theory behind this?

4. Thanks,
Zak

P.S. It's easy to do it with k=186,
just prepend 186 to 865625^2:
    865625^2 =
   749306640625 and 
186749306640625=13665625^2