We prove that every integer n⩾10 such that n≢1 mod 4 can be written as the sum of the square of a prime and a square-free number. This makes explicit a theorem of Erdős that every sufficiently large integer of this type may be written in such a way. Our proof requires us to construct new explicit results for primes in arithmetic progressions. As such, we use the second author’s numerical computation regarding the generalised Riemann hypothesis to extend the explicit bounds of Ramaré–Rumely.
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机译：我们证明，每个n⩾10使得n such1 mod 4可以写为素数平方和无平方数的和。这明确表明了鄂尔多斯定理，即这种类型的每个足够大的整数都可以这样写。我们的证明要求我们为算术级数的素数构造新的显式结果。因此，我们使用第二作者关于广义Riemann假设的数值计算来扩展Ramaré–Rumely的显式范围。
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