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Re: Maximum number not represented by algebraic equation
Posted:
Jul 21, 1996 8:32 PM
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In article <DuuIID.E37@watdragon.uwaterloo.ca>, Kelly B. Roach (kbroach@daisy.uwaterloo.ca) writes:
>as the only nonsolutions, 43 being the largest.
> Concerning the more abstract a*x+b*y+c*z, I don't have
>much to say and will leave this question to someone else.
Assume a is smallest "size",
If b = B mod a and
c = C mod a
Look for l_s*B + m_s*C = s mod a, s = 1,2,3,.....,a-1, choosing
numerically smallest l,m in each case
If equation cannot be solved for one or more s then there is no
largest unattainable number.
Find largest l_s*b +M_s*c and add multiples of a to others to
obtain consecutive numbers congruent 0,1,.. a-1 mod a, including
l_s*b + m_s*c.
Take away multiples of a, if possible, until highest unattainable
number is reached.
Iain Davidson Tel : +44 1228 49944
4 Carliol Close Fax : +44 1228 810183
Carlisle Email : iain@stt.win-uk.net
England
CA1 2QP
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