- #1
Albert1
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$b,k\in N$ and $\sqrt {b^2(k-3)(k+1)-4k}$ also $\in N$
find all possible $k$
find all possible $k$
Albert said:$b,k\in N$ and $\sqrt {b^2(k-3)(k+1)-4k}$ also $\in N$
find all possible $k$
kaliprasad said:putting k-2 = a for getting simpler expression we have
$b^2(k-3)(k+1)-4k$
=$b^2(a-2)(a+2)-4(a+1)$
= $b^2(a^2-4)-4(a+1)$
= $a^2b^2 - 4a -4(b^2+1)$
to solve for a
for it to to be perfect square discriminant has to be zero
but 16 + 16b(b^2+1) >0 so no solution
greg1313 said:b = 1, k = 7.
"Finding All Possible $k$ for $b,k\in N$" refers to the process of determining all the possible values of $k$ that satisfy the conditions that $k$ and $b$ are both natural numbers.
It is important to find all possible $k$ for $b,k\in N$ because it allows for a comprehensive understanding of the range of values that can fulfill the given conditions. This information can be useful in various mathematical and scientific applications.
Common techniques used to find all possible $k$ for $b,k\in N$ include listing out all possible combinations of $b$ and $k$ values, using algebraic equations and manipulations, and using computer algorithms or programs.
Yes, there are restrictions on the values of $b$ and $k$ in "Finding All Possible $k$ for $b,k\in N$". Both $b$ and $k$ must be natural numbers, which means they can only be positive integers (including zero).
"Finding All Possible $k$ for $b,k\in N$" can be applied in various fields such as cryptography, number theory, and combinatorics. It can also be used to solve mathematical problems and equations, and to analyze and understand patterns and relationships in data.