How to solve this special case of Fredholm Integral Equation of the First Kind

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General form of 'Fredholm Integral Equation of the First Kind'

$f(x) = \int_a^b{K(x,t)\phi(t)} dt$

Where $\phi(t)$ is the unkown

My special case is

$1 = \int_a^b{k(t)\phi(t)} dt$

A trivial solution is of course

$\phi(t) = \frac{1}{\int_a^b k(t)dt} $

I wonder whether there are some general nontrivial solutions.