Re: A REAL TOUGH PROBLEM

• To: mathgroup at smc.vnet.net
• Subject: [mg15368] Re: [mg15343] A REAL TOUGH PROBLEM
• From: BobHanlon at aol.com
• Date: Sat, 9 Jan 1999 23:58:24 -0500
• Sender: owner-wri-mathgroup at wolfram.com

```In a message dated 1/8/99 9:36:46 AM, root at nntpb.cb.lucent.com writes:

>Let
>
>P(m) = a1^m + b1^m + c1^m
>Q(m) = a2^m + b2^m + c2^m
>R(m) = a3^m + b3^m + c3^m
>S(m) = a4^m + b4^m + c4^m
>
>Z(m) = (P(m)^2 - Q(m)^2) / (R(m)^2 - S(m)^2)
>
>where a1,a2,a3,a4,b1,b2,b3,b4,c1,c2,c3,c4 are all Integers.
>
>Find the solution for a1,a2,a3,a4,b1,b2,b3,b4,c1,c2,c3,c4 when
>
>Z(3) = Z(5)
>

One obvious solution would be for Z[m] = 0, i.e., P[m] = Q[m] and R[m]
<> S[m]

Clear[P, Q, R, S, Z, a1, a2, a3, a4, b1, b2, b3, b4, c1, c2, c3, c4];

a2 = a1; b2 = b1; c2 = c1;
P[m_] := a1^m + b1^m + c1^m;
Q[m_] := a2^m + b2^m + c2^m;
R[m_] := a3^m + b3^m + c3^m;
S[m_] := a4^m + b4^m + c4^m;
Z[m_] := (P[m]^2 - Q[m]^2)/(R[m]^2 - S[m]^2)

Z[m]

0

Then the values for {a1, a3, a4, b1, b3, b4, c1, c3, c4} are arbitrary
integers as long as R[m] <> S[m].
Consequently, there are infinitely many solutions.  You would need to
have more constraints than just Z[3] = Z[5].

Bob Hanlon

```

• Prev by Date: Integrate in Mathematica 2.2 and 3.0
• Next by Date: listplot and notebook directory
• Previous by thread: A REAL TOUGH PROBLEM
• Next by thread: Re: A REAL TOUGH PROBLEM