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GCD & LCMhard
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The Diophantine equation 3x+5y=203x + 5y = 203x+5y=20 has integer solutions. One particular solution is (x0,y0)=(5,1)(x_0, y_0) = (5, 1)(x0​,y0​)=(5,1). The general solution is x=5+5tx = 5 + 5tx=5+5t, y=1−3ty = 1 - 3ty=1−3t for integer ttt. How many solutions (x,y)(x, y)(x,y) satisfy the equation AND 0≤x≤200 \le x \le 200≤x≤20?