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You have N = kd+7 and 5N = pd+10 for integers k & d. Thus 5kd+35 = pd + 10 and d must divide 25 (why?) Thus d = 1, 5 or 25. Dividing N by d leaves a remainder of 7 so that d couldn't be 1 (why?). Dividing 5N by d leaves a remainder of 10 so that d couldn't be 5 (why?). Thus ...? Penny  


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