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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.
Two sessions of swimming lessons were held at a pool. In the first session 40 students attended. Of these 40 students 60% were girls. How many girls attended the first session of s
Let R be the relation on S = {1, 2, 3, 4, 5} defined by R = {(1,3); (1, 1); (3, 1); (1, 2); (3, 3); (4, 4)}. (b) Write down the matrix of R. (c) Draw the digraph of R.
NUMBER SYSTEMS: Numbers are intellectual witnesses that belong only to mankind. Example: If the H C F of 657 and 963 is expressible in the form of 657x + 963 x -
Proof for Properties of Dot Product Proof of u → • (v → + w → ) = u → • v → + u → • w → We'll begin with the three vectors, u → = (u 1 , u 2 , ...
Recognizes the absolute extrema & relative extrema for the given function. f ( x ) = x 2 on [-2, 2] Solution Following is the graph for this fun
There is a number. If the sum of digits is 14, and if 29 is subtracted from the number, the digits become equal. Find the number.
Find out the least number of cables required to connect 100 computers to 20 printers to assurance that 20 computers can directly access 20 different printers. Justify your answer.
into how many smaller part is each centimeter divided
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