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N^4 and N^2 (Posted on 2023-09-09) Difficulty: 3 of 5
Find as many positive integers, N, not ending in 0, as you can, such that N^2 contains N and N^4 contains N^2.

See The Solution Submitted by K Sengupta    
Rating: 5.0000 (1 votes)

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Solution Computer solution Comment 1 of 1
1 1 1
5 25 625
25 625 390625
90625 8212890625 67451572418212890625

Not in oeis.
------------------------
ns = [i for i in range(1,100001) if str(i)[-1] != '0']
squares = [i*i for i in ns]
fourths = [i*i for i in squares]

for i,f in enumerate(ns):
    if str(f) in str(squares[i]) and str(squares[i]) in str(fourths[i]):
        print(ns[i], squares[i], fourths[i])

  Posted by Larry on 2023-09-09 09:20:53
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