A nucleotide composition constraint of genome sequences. Zhang CT, Zhang R. Comput Biol Chem. 2004 Apr;28(2):149-53. PMID: 15130543
For the base frequences in a DNA a, c, g, t, they define:
S = a2 + c2 + g2 + t2
Then they claim:
S = ½ + ½ (a - t)2 + ½ (g - c)2 - (a + t)(g + c)
Your challenge: Prove their claim.