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Excerpt from Carl Friedrich Gauss Werke, Vol. 2
Quoties igitur %(k - 1)(p - 1) par evadit, quod fit, si vel uterque k, vel sal tem alteruter est formae 4n+1 necessario (k, p) et (p, k) vel ambo pares vel ambo impares esse debent. Quoties autem %(k - 1)(p - l) impar est, quod eve nit, si uterque k, est _formae 4n +3, necessario alter numerorum (k, p), p, k) par, alter impar esse debebit. In casn priori itaqne relatio ipsins k ad et re letio ipsins ad k (quatenus alter alterius residuum vel non-residuum est) iden ticae crunt, in casn posteriori 0ppositae.
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