Parnost u matematici je osobina pripadnosti cijelog broja u jednu od dvije grupe: u parne ili neparne brojeve. Cijeli broj je paran ako je višekratnik broja 2, odnosno ako je djeljiv brojem 2 bez ostatka, a neparan ako nije paran. Brojevi koji nisu cijeli nisu ni parni ni neparni.
Primjeri parnih brojeva su -6, 0, 14, 1360, a neparnih -13, 1, 9, 427. Posebice, nula je paran broj.
Formalno, parni brojevi su svi brojevi oblika 2k gdje je k cijeli broj, a neparni svi oblika 2k+1. Zapisano simbolima, skupovi parnih i neparnih brojeva definirani su s
Neka je
paran, a
neki neparan cijeli broj. Tada vrijedi:
![{\displaystyle P+P=P}](http://178.128.105.246/host-https-wikimedia.org/api/rest_v1/media/math/render/svg/d5a3f7c3d3d7f8b5170a631ebef48364e003b7ee)
![{\displaystyle P+N=N}](http://178.128.105.246/host-https-wikimedia.org/api/rest_v1/media/math/render/svg/8517dd1c62d7b0f221ae92e7c301148775c1808a)
![{\displaystyle N+P=N}](http://178.128.105.246/host-https-wikimedia.org/api/rest_v1/media/math/render/svg/69a3fce32a1225f90bbb60e486bf87f65d359a27)
![{\displaystyle N+N=P}](http://178.128.105.246/host-https-wikimedia.org/api/rest_v1/media/math/render/svg/b827574f7a4cdca77d4666a5f717452224e9e938)
![{\displaystyle P-P=P}](http://178.128.105.246/host-https-wikimedia.org/api/rest_v1/media/math/render/svg/3a923c42a27bf213ed625ca29960c6b3c92b3a0c)
![{\displaystyle P-N=N}](http://178.128.105.246/host-https-wikimedia.org/api/rest_v1/media/math/render/svg/0a22bbdc316945bae722c31bafda09aac3a55459)
![{\displaystyle N-P=N}](http://178.128.105.246/host-https-wikimedia.org/api/rest_v1/media/math/render/svg/a526f622ec26b880d93dbeaf0040eda4d4c3be1d)
![{\displaystyle N-N=P}](http://178.128.105.246/host-https-wikimedia.org/api/rest_v1/media/math/render/svg/d4ff4c9d3e1c6659448bb0fd48cd58369c4e754c)
![{\displaystyle P\cdot P=P}](http://178.128.105.246/host-https-wikimedia.org/api/rest_v1/media/math/render/svg/f2864c6aaa68c1def8736f1a219dd01572550db9)
![{\displaystyle P\cdot N=P}](http://178.128.105.246/host-https-wikimedia.org/api/rest_v1/media/math/render/svg/df5043c42b7da561a2edea616495868640803143)
![{\displaystyle N\cdot P=P}](http://178.128.105.246/host-https-wikimedia.org/api/rest_v1/media/math/render/svg/54ce6bf4ef6cc5e4fec0ac950add3c109e93384e)
![{\displaystyle N\cdot N=N}](http://178.128.105.246/host-https-wikimedia.org/api/rest_v1/media/math/render/svg/4ff60ca751fc2205900e7ee45ed970ae1fbaa6a7)
,
![{\displaystyle P/N=P}](http://178.128.105.246/host-https-wikimedia.org/api/rest_v1/media/math/render/svg/e106ce4e193fbb3c54df94bb415ce61b62d23e55)
![{\displaystyle Z}](http://178.128.105.246/host-https-wikimedia.org/api/rest_v1/media/math/render/svg/1cc6b75e09a8aa3f04d8584b11db534f88fb56bd)
![{\displaystyle N/N=N}](http://178.128.105.246/host-https-wikimedia.org/api/rest_v1/media/math/render/svg/dc3e122e9a224d1dffdbf2036b3f36fdb342b4e3)
Napomene:
- Uvjet je da je brojnik višekratnik nazivnika.
- Nazivnik ne smije biti
.