Hensel's lemma the value of "c" mod 27: if "c" ≡ 1 mod 27 then use "a" = 1, if "c" ≡ 10 mod 27 then use "a" = 4 (since 4 is a root of "f"("x") mod 27), and if "c" ≡ 19 mod 27 then use "a" = 7. (It is not true that every "c" ≡ 1 mod 3 is a 3-adic cube, e.g., 4 is not a 3-adic cube since it is not a cube mod 9.) In a similar way, after some preliminary work Hensel's lemma can be used to show that for any "odd" prime number
Doubling the cube at solving what they saw as an obstinate but soluble problem. However, the nonexistence of a solution was finally proven by Pierre Wantzel in 1837. In algebraic terms, doubling a unit cube requires the construction of a line segment of length , where ; in other words, . This is because a cube of side length 1 has a volume of , and a cube of twice that volume (a volume of 2) has a side length of the cube root of 2. The impossibility of doubling the cube is therefore equivalent to the statement that is not a constructible