100 ...
121, 144, 169, 196, 225
256, 289, 324, 361, 400
441, 484
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121 and 196
36, 49, 64 and 81
64 and 36.
How about: 100-64 = 36 as one example
Perfect squares have odd numbers of factors. The perfect squares less than 100 are: 1,4,9,16,25,36,49,64,81,100. 64 seems to fit both criteria.