Difference between revisions of "1998 CEMC Gauss (Grade 7) Problems/Problem 25"
Coolmath34 (talk | contribs) (Created page with "== Problem == Two natural numbers, <math>p</math> and <math>q,</math> do not end in zero. The product of any pair, <math>p</math> and <math>q,</math> is a power of 10 (that i...") |
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== Solution == | == Solution == | ||
− | If the product <math>pq</math> is a power of <math>10,</math> then <math>p</math> must be in the form <math>5^n</math> and <math>q</math> must be in the form <math>2^n.</math> | + | If the product <math>pq</math> is a power of <math>10,</math> and both <math>p</math> and <math>q</math> do not end in 0, then <math>p</math> must be in the form <math>5^n</math> and <math>q</math> must be in the form <math>2^n.</math> |
Start looking at small values of <math>n</math> and subtract: | Start looking at small values of <math>n</math> and subtract: |
Revision as of 17:50, 7 April 2024
Problem
Two natural numbers, and
do not end in zero. The product of any pair,
and
is a power of 10 (that is, 10, 100, 1000, 10 000 , ...). If
, the last digit of
cannot be
Solution
If the product is a power of
and both
and
do not end in 0, then
must be in the form
and
must be in the form
Start looking at small values of and subtract:
This pattern continues in groups of , and the only number not included is
-edited by coolmath34