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How does this program work ?

Let's take the case of (6,2,5).

We need to solve the equation:

For 6th power, we have the relations:

These relations are **very** important.

Now, we can deduce some restrictions on **a**, **b**, **c**, **d**,
**e**, **f** and **g** !

The first one is that **a **and **b** cannot be both multiple of 2, 3
or 7.

If **a **and **b** were both multiple of 2 for example, then **c**,**
d**,** e**,** f **and **g** are necessarily multiple of 2, so all
terms are multiple of 2 and the solution is not primitive.

We will try to find **c **and **d **that can be related to **a **and
**b**.

Let's enumerate the conditions on **a **and **b **modulo 7.

1) if **a ^{6} **= 0 mod 7 and

2) if **a ^{6} **= 0 mod 7 and

or:

3) if **a ^{6} **= 1 mod 7 and

or:

4) if **a ^{6} **= 1 mod 7 and

And we have now:

There is a wonderful trick that can be used there !!!

Suppose that we have **a**, **b** and **c** then we can deduce **d**
because **a ^{6}+b^{6}-c^{6}-d^{6} is divisible
by 7^{6}**

This is done by using a table of residues modulo

**More informations coming soon.**