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Changing form (
Posted on 20130629
)
Define a product a*b with a and b not necessarily distinct integers in {2,3,4,...}.
Show that a*b is always expressible as xy + xz + yz + 1, with x, y, and z positive integers.
Source: rephrased Putnam competition.
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Submitted by
Ady TZIDON
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Transformation (spoiler)
Comment 1 of 1
Let x = a1
y = b1
z = 1
Then ab = (x+1)(y+1)
= xy + x + y + 1
= xy + xz + yz + 1
q.e.d
Posted by
Steve Herman
on 20130629 20:33:30
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