1819. 
Bernardo chooses a threedigit positive integer and writes both its base5 and base6 representations on a blackboard. Later LeRoy sees the two numbers Bernardo has written. Treating the two numbers as base10 integers, he adds them to obtain an integer . For example, if , Bernardo writes the numbers and , and LeRoy obtains the sum . For how many choices of are the two rightmost digits of , in order, the same as those of ?
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