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Topic: Maximum number not represented by algebraic equation
Replies: 1   Last Post: Jul 21, 1996 8:32 PM

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Iain Davidson

Posts: 189
Registered: 12/6/04
Re: Maximum number not represented by algebraic equation
Posted: Jul 21, 1996 8:32 PM
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In article <>, Kelly B. Roach ( 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 :

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