16. Prove that an integer (a,-1an-2 · . . ao)10 is divisible by 11 if and only if ao + a2 + a4 + . . . = aj + a3 + a5 + · ·. (mod 11). [Hint: 10 = -1 (mod 11).] %3D

Q: 23. For any real number a, a ‡ 0, show that a +1 a +4 a +7 a +5 a+6 a +9 a -2 a +3 and a +8 | = 0, a…

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Q: Find a positive integer less than 8 for x that satisfies x = 720 + 3 (mod 7).

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Q: For any real number a, a ≠ 0, show that a+4 a+7 a+5 a +8 = 0, a+6 а+9 a+1 a+2 a+3 and 4a7a 5a 8a =…

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Q: Prove that 5 does not divide 5n+3 for any integer n.

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Q: Prove that a number in the form 6k+5,” what I mean is a number in the form of 6 times some integer…

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Q: (b) Prove that any odd number is expressible in the form 4n + 1 or 4n + 3 where n is an integer.

A: Number System

Q: at any positive odd integer is of the

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Q: Given any real numbers a and d, consider the expression (a + md) + (a + (m + 1)d) + (a + (m + 2)d) +…

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Q: Show that /2, /3, 5 cannot be the terms of a single A.P.

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Q: Prove that A2=I.

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Q: Disprove the statement: There is a real number x such that xº +x* +1 = 2x².

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Q: Prove that an odd number multiplied by an odd number is odd.

A: The objective is to prove that an odd number multiplied by an odd number is odd.

Q: In Problems 70. a hemisphere of radius a has its base on the xy-plane, centered at the origin; the…

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Q: 2 4. Express 989 = 23 43 in the form x² + xy + 5y².

A: The given number is 989. The objective is to express the given number in the form of x2+xy+5y2.

Q: x² + 4x = 10(mod11) (mod11) X=

A: Given that x2+4x≡10 (mod 11)x2+4x+4≡10+4 (mod 11)x2+4x+4≡14 (mod 11)x2+4x)(x+2)2≡14+11 (mod…

Q: 6. Letn be a positive integer. Prove that 1+ 4+7++ (3n − 2) = = 3n² 2

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Q: "Every positive integer can be written as the sum of the square of 3 positive integers." prove…

A: Given: "Every positive integer can be written as the sum of the square of 3 positive integers." To…

Q: fermat's theorm states, if p is prime & a is a positive integer not divisible by p then-------- and…

A: Fermat's Theorem: If p is a prime and a is a positive integer and not divisible by the prime p, then…

Q: x² - 2x = 8(mod19) X= (mod19)

A:

Q: fermat's theorm states, if p is prime & a is a positive integer not divisible by p then-------- and…

A: Fermat's states that if p is a prime and a is a positive integer not divisible by p, than ap-1≡1 mod…

Q: Show that if k is a positive integer, then (15k+4)/(10k+3) is in lowest terms.

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Q: I need help

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Q: √38 10 V √ 65

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Q: Let Find formulas for the entries of M", where n is a positive integer. Hint: a formula such as 5…

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Q: Let n be an integer, use the definition of even to prove that 10n+ 4 is even. 10n+4=0x0 Since is a…

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Q: 5x² + 3x = 3(mod17) X = (mod17)

A: Given that 5x2+3x≡3 (mod 17)x(5x+3)≡3 (mod 17)x≡3 (mod 17)  or   (5x+3)≡3 (mod 17)x≡3 (mod 17)  or…

Q: 5 13 √194

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Q: Give all non-negative solutions for 10r =-17 mod 4.

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