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Find all integers

Source: Indian RMO 2002 Problem 7

October 27, 2005

Problem Statement

Find all integers a,b,c,da,b,c,d such that (i) 1≤a≤b≤c≤d1 \leq a \leq b \leq c \leq d; (ii) ab+cd=a+b+c+d+3ab + cd = a +b +c +d + 3.
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