8 Number Theory Problems with Modular Equations Types

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• Question.pdf

8) 500!/200!= 201*202*…*500
We notice the following pattern: the product of ten consecutive numbers starting from 201 to 210 ends in two zeros (one comes from 202*205 and the 2nd from the 10th number – 210). This pattern holds up to 291*…*300 (where we have three 0’s instead). Then, between 301*..*310 and so on (up to 400) the same number of 0’s occurs....

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