For example for an isolated system the energy $E$ is conserved. But then any function of energy, (like $E^2,\sin E,\frac{ln|E|}{E^{42}}$ e.t.c.) is conserved too. Therefore one can make up infinitely many conserved quantities just by using the conservation of energy.
Why then one can usually hear of "system having N constants of motion"? "System having only one constant of motion"?
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