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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.
Equal-sharing - situations in which we need to find out how much each portion Multiplication and Division contains when a given quantity is shared out into a number of equal porti
two sides of an equilateral triangle have lengths 3x-1 and 3x-1. Which of 27-x or 2x-4 could be the length of the third side?
Critical point of exponential functions and trig functions, Let's see some examples that don't just involve powers of x. Example: find out all the critical points for the
suresh invested rs.1080 in shares of face value rs.50 at rs.54.After receiving dividend on them at 8% he sold them at 52.In each of the transaction he paid 2 % brokerage.Hpw much d
Find the largest possible positive integer that will divide 398, 436, and 542 leaving remainder 7, 11, 15 respectively. (Ans: 17) Ans: The required number is the HCF of the n
The sum of the digit number is 7. If the digits are reversed , the number formed is less than the original number. find the number
What is the ratio of the areas of sectors I and II ? (Ans:4:5) Ans: Ratio will be 120/360 Π r 2 : 150/360 Π r 2 4/12 : 5/12 =
There are 81 women teachers at Russell High. If 45% of the teachers in the school are women, how many teachers are there at Russell High? Use the proportion part/whole = %/100.
ALGORITHM FOR DIVISION : If you ask a 10 or 1 1-year-old child to solve, say, 81 + 9, the chances are that she will correctly do it. But if you ask her to solve, say 72 + 3, t
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