Difference between revisions of "1980 Canadian MO Problems/Problem 1"
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Latest revision as of 20:52, 14 December 2011
Problem
If is the decimal expansion of a number in base
, such that it is divisible by
, determine
.
Solution
Write as
, for some integer
. Since
, we look at this equation
, then
.
Looking at the equation :
Thus, .
Substituting into the equation, and looking at the equation
:
Thus, .
Thus, we get the 5 digit number , which is indeed divisible by
, thus satisfying requirements. Thus,
.
See also
1980 Canadian MO (Problems) | ||
Preceded by First Question |
1 • 2 • 3 • 4 • 5 | Followed by Problem 2 |