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1. Suppose n ≡ 7 (mod 8). Show that n ≠ x 2 + y 2 + z 2 for any x, y, z ε Z. 2. Prove ∀n ε Z, that n is divisible by 9 if and only if the sum of its digits is divisible by 9.
Construct the finite automaton for the state transition table given below. Ans: The finite automata is displayed below. The initial state is marked along with arrow sign a
The Geometric Index or Industrial Share index The Geometric Index or Industrial Share index is an index of 30 selected top industrial companies. This is calculated by taking a
types of brands
what is limit
On your geometry test you have two triangles: ?ABC and ?MNO. You are told that ?A ? ? M and that ?B ? ? N. Which statement is also true?
(a) An unordered pair fm; ng with 1 ≤ m ≠ n ≤ 6 is called a duad. List the 15 duads. (b) There are 15 ways to partition {1, ......, 6 } into 3 duads, such as { {1; 2}, {3, 4},
Evaluate following limits. Solution In this part what we have to note (using Fact 2 above) is that in the limit the exponent of the exponential does this, Henc
Taking 2^x=m and solving the quadratic for getting D>=0 we get range= [3/4 , infinity )
Give the Proofs in Mathematics ? 1 Two-column deductive proof Proof: Statements Reasons * Start with given c
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