Unformatted text preview: k there exist k consecutive integers each of which is divisible by a square. Exercise 5. 2.3.36: Find the last two decimal digits of 2 1000 and 3 1000 . Exercise 6. 2.6.2: Solve the congruence x 5 + x 4 + 1 ≡ 0(3 4 ) . Exercise 7. 2.6.11: Let p be a prime and f ( x 1 , x 2 , . . . , x n ) be an integer polynomial in n variables, and suppose that f ( a 1 , . . . , a n ) ≡ 0( p ) and that the partial derivative ∂f ∂x i ( a 1 , . . . , a n ) ±≡ 0( p ) . Show that the congruence f ( x 1 , . . . , x n ) ≡ 0( p j ) has a solution for each j ....
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 Spring '08
 Humphreys,G
 Prime number, ﬁve lowest scores

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