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Click and drag the given steps (on the right) to their corresponding step names (on the left) to prove that if al band bl c,
Click and drag the given steps (on the right) to their corresponding step names (on the left) to prove that if al band bl c, then alc Step 1 By definition of divisibility, c a(ts), with ts being an integer, implies alc. Suppose alband bl c. By definition of divisibility, a I b means that a- btfor some integer t, and blc means that b- cs for some integer s. Suppose al band bl c. By definition of divisibility, a b means that a-bt for some integer t, and blc means that b-cs for some integer s Step 2 We substitute the equation b-cs into a-bt and get a cst We substitute the equation b cs into a - bt and get a-csit Suppose al band bl c. By definition of divisibility, a I b means that b-at for some integer t, and blc means that c- bs for some integer s. Step 3 We substitute the equation b- at into c-bs and get c-ats By definition of divisibility, a - c(st), with ts being an integer, implies al c. By definition of divisibility, a-c(st, with ts being an integer, implies al c
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