MHBCan $S_5$ be written as a multiple of $S_3$ and $S_2$?
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The discussion centers on proving the equation $\frac{S_5}{5}=\frac{S_3}{3}\cdot\frac{S_2}{2}$ given that $S_n=x^n+y^n+z^n$ and $S_1=0$, which implies $x+y+z=0$. The proof involves manipulating the expressions for $S_5$, $S_3$, and $S_2$ using algebraic identities and relationships derived from the condition $S_1=0$. The calculations show that $S_5$ can be expressed in terms of $S_3$ and $S_2$, ultimately confirming the desired equation. The proof concludes successfully with the established relationship.
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anemone
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Let $$S_n=x^n+y^n+z^n$$. If $$S_1=0$$, prove that $$\frac{S_5}{5}=\frac{S_3}{3}\cdot\frac{S_2}{2}$$.
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A power has two parts. Base and Exponent.
A number 423 in base 10 can be written in other bases as well:
1. 4* 10^2 + 2*10^1 + 3*10^0 = 423
2. 1*7^3 + 1*7^2 + 4*7^1 + 3*7^0 = 1143
3. 7*60^1 + 3*60^0 = 73
All three expressions are equal in quantity. But I have written the multiplier of powers to form numbers in different bases. Is this what place value system is in essence ?