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# Diophantine equations

Posted 10 years ago
 Hi, I need to help with solution of diofantine equations 4x+2y=28 in Integers. If I find Documentation Center, it say: Reduce[4x+2y==28,{x,y},Integers]. But the result is not expressed with the parameter C like in the picture. THANKS A LOT!
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Posted 10 years ago
 You can try another function:Solve[4 x + 2 y == 28, {x, y}, Integers]and receive{{x -> ConditionalExpression[C[1], C[1] [Element] Integers], y -> ConditionalExpression[14 - 2 C[1], C[1] [Element] Integers]}}
Posted 10 years ago
 She searches for integer solutions and does not believe that the expressions given are integer. Mathematica is also not sure about that: In[51]:= Clear[x, y] x[n_] := 1/2 ((8 - 3 Sqrt[7])^n + (8 + 3 Sqrt[7])^n) y[n_] := -(((8 - 3 Sqrt[7])^n - (8 + 3 Sqrt[7])^n)/(2 Sqrt[7])) In[68]:= RootApproximant[x[#]] & /@ RandomInteger[{1, 30}, 17] Out[68]= {2024, 2199950293420883836928, 2024, \ 2325668404237133588966684445638656, 2261936092886171715528294400, \ 2261936092886171715528294400, 8, 2261936092886171715528294400, 1/2 (134255446617603 + Sqrt[ 18024524946491071433658089473]), 574522862194843517270624305152, \ 2024, 8193151, 2199950293420883836928, 558778713173023503941632, 8, \ 37064767922732740871188780993740800, \ 2325668404237133588966684445638656} In[69]:= RootApproximant[y[#]] & /@ RandomInteger[{1, 30}, 17] Out[69]= {12535521795, 194307, 765, 13625260145284696589750763520, \ 13625260145284696589750763520, 3096720, 854931483328272233719136256, \ 12192, 765, 831503053299319046144, 3183973182717, \ 3460762433314345591306287316992, 786554688, \ 854931483328272233719136256, 3, 3365924154344798473420800, 48} and going up to 30 is not so far.  In[72]:= FactorInteger[18024524946491071433658089473] Out[72]= {{151, 1}, {2577984271, 1}, {46302732029905513, 1}} In[73]:= 151 2577984271 == 46302732029905513 Out[73]= False Indeed not a square of something.By the way, Martina, the solution appears exactly as announced by the manual: In[48]:= Reduce[x^2 - 7 y^2 == 1 && x > 0 && y > 0, {x, y}, Integers] Out[48]= C[1] \[Element] Integers && C[1] >= 1 && x == 1/2 ((8 - 3 Sqrt[7])^C[1] + (8 + 3 Sqrt[7])^C[1]) && y == -(((8 - 3 Sqrt[7])^C[1] - (8 + 3 Sqrt[7])^C[1])/(2 Sqrt[7])) The linear equation has of course also a constant, but this is pointless,isn't it? In[74]:= Reduce[4 x + 2 y == 28, {x, y}, Integers] Out[74]= C[1] \[Element] Integers && x == C[1] && y == 14 - 2 C[1] 
Posted 10 years ago
 Are you interested in the linear or quadratic equation? Also, what would be a form of result that you are trying to obtain?
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