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Number TheoryQuestion and Answers: Page 14
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Question and Answers Forum |
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Number TheoryQuestion and Answers: Page 14 |
| A positive integer such as 4334 is a palindrome if it reads the same forwards or backwards. What is the only prime palindrome with an even number of digits? |
| for m,n positive integers m > n prove that lcd(m,n) + lcd(m+1,n+1) > ((2mn)/(√(m−n))) |
| A transformation f on a complex plane is defined by z′ = (1 +i)z −3 + 4i show that f is a simultitude with radius r and centre Ω to be determined. Determine to the invariant point under f. |
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| what is the number of ordered pairs of positif integers (x,y) that satisfy x^2 +y^2 −xy=37 |
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| Determine x,y ∈ Z such that 1+2^x +2^(2x+1) = y^2 |
| solve for x,y ∈ N 7^y +2 = 3^x |
| what is remainder of 2^7^(2002) divided by 352 |
| find integral solution of y^2 = x^3 +1 |
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| what is number of positive integral solutions of 10xy+7x+3y = 2077829313 |
| If x and y are integers , prove that x^3 −7x divisible by 3 |
| Determine all pairs (x,y) of integers satisfying 1+2^x +2^(2x+1) =y^2 |
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| Show that RE[(1/(1−z))]=(1/2) where z = cos θ + i sinθ |
| Given that ω = e^(iθ) , θ≠ nπ , n ∈N show that (1 + ω)^n = 2^n ((1/2)θ)e^((1/2)(inθ)) please help me out on this, i′ve stumbled on it. |
| 69x ≡ 1 (mod 31) solve for x |
| Let m and n be two positive integers satisfy (m/n) = (1/(10×12))+(1/(12×14))+(1/(14×16))+...+(1/(2012×2014)) find the smallest possible value of m+n |
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| find all pairs of integer for xy+3x−4y = 29 |
| If x∈C . find solution of 3+i(√2) = e^(ix) |
| 5^(10) (mod 11)=? |
| find x such that x≡3 (mod5) x≡5 (mod7) x≡7(mod11) |
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| Prove by set theory or otherwise lcm( gcd(x,y),gcd(y,z),gcd(z,x) ) is equal to gcd( lcm(x,y),lcm(y,z),lcm(z,x) ) Or give a counter example. |